Synopsis: A Riemann calculator?

Calculus, group theory, and other mathematical tools are indispensable for understanding physics. Now the tables may be turned in a new approach toward solving a long-standing problem in mathematics.
Synopsis figure

Perhaps the greatest unsolved problem in mathematics is the Riemann hypothesis, which states that the nontrivial zeros of the zeta function all have a real part equal to 1/2. Many results in mathematics, through their relation to the distribution of prime numbers, are based on whether the hypothesis is correct.

One possible route to a proof of the hypothesis is to find a quantum mechanical system whose quantized energy levels yield the nontrivial zeros of the zeta function. About a decade ago, it was conjectured that the correct quantum system is related to a particular classical system that exhibits chaotic dynamics. Writing in Physical Review Letters, Germán Sierra from CSIC-UAM in Spain and Paul Townsend from the University of Cambridge extend part of this classical model to a realistic quantum mechanical system: a charged particle moving in a plane in a uniform magnetic field and a saddle-shaped electric potential. Although it is not a proof of the Riemann hypothesis, Sierra and Townsend’s idea makes an interesting connection between a physical system—similar to the one in which the quantum Hall effect was measured—and efforts to solve a long-standing mathematical problem. – Sonja Grondalski


Features

More Features »

Announcements

More Announcements »

Subject Areas

Interdisciplinary Physics

Previous Synopsis

Magnetism

Chiral contortions

Read More »

Next Synopsis

Related Articles

Focus: Astronomy Students Not Learning the Basics
Interdisciplinary Physics

Focus: Astronomy Students Not Learning the Basics

Nearly half of middle school students in a Norwegian study thought that planets are bigger than stars, even after astronomy instruction. Read More »

Synopsis: Social Determinants of Epidemic Growth
Complex Systems

Synopsis: Social Determinants of Epidemic Growth

A new network model reveals that social mixing and mobility can determine the areas of a city that are critical in provoking an epidemic outbreak. Read More »

Focus: Identifying Early Signs of Online Extremist Groups
Complex Systems

Focus: Identifying Early Signs of Online Extremist Groups

An analogy between the growth of online networks and the formation of gels suggests ways to detect extremist groups before they become influential. Read More »

More Articles